MatricesHard
Question
Let M and N be two 3 × 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)-1 (MN-1)T is equal to
Options
A.M2
B.-N2
C.-M2
D.MN
Solution
MN = NM
M2N2(MTN)-1(MN-1)T
M2N2N-1(MT)-1(N-1)T.MT
= M2N.(MT)-1(N-1)TMT = - M2.N(M)-1(NT)-1MT
= + M2NM-1N-1MT = - M.NMM-1N-1M = - MNN-1M = - M2.
Note: A skew symmetric matrix of order 3 cannot be non-singular hence the question is wrong.
M2N2(MTN)-1(MN-1)T
M2N2N-1(MT)-1(N-1)T.MT
= M2N.(MT)-1(N-1)TMT = - M2.N(M)-1(NT)-1MT
= + M2NM-1N-1MT = - M.NMM-1N-1M = - MNN-1M = - M2.
Note: A skew symmetric matrix of order 3 cannot be non-singular hence the question is wrong.
Create a free account to view solution
View Solution FreeMore Matrices Questions
If A, B are two matrices such that A + B = , A − B = then AB equals -...If A is a non-singular matrix and B is any matrix satisfying AB - BA = A, then -...A matrix A = (aij) m × n is said to be a square matrix if -...If A = and f(x) = 2x2 − 3x, then f(A) equals -...If Ai = and if |a|<1, |b|<1, then (Ai) is equal to-...